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Constructing quasi-breathers in 𝛽-FPUT chain with the aid of genetic algorithm
In this work, a simple genetic algorithm (GA) is used to find and characterize different QBs in a 𝛽-FPUT chain. By considering the space of initial particle displacements as a global optimization landscape, GA maximizes the energy localization function by automatically evolving candidate states toward highly localized long-lived solutions without a priori symmetry assumptions. 200 QBs with an oscillation frequency higher than the phonon spectrum were obtained and the distributions of their parameters were analyzed. The distributions of the localization parameter, amplitude, and frequency have two peaks, which means that GA generates two groups of QBs with small and large values of these parameters. QBs are stationary or move with a symmetrical velocity distribution, so the probability that QB moves to the right or to the left is equal. Symmetric QBs, such as the Sievers-Takeno mode, can be obtained using a constrained GA search. This method can be easily extended to 2D and 3D lattices, offering an artificial intelligence pathway for designing energy localization in crystals, phononic, mechanical and metamaterial systems.